Lazy Evaluation of Geometric Definitions of Objects Within Procedural Programming Environments

ABSTRACT

This description provides tools for lazy evaluation of geometric definitions of objects within procedural programming environments. Computer-based methods provided by these tools may parse input program code that includes statements that are syntactically consistent with a procedural programming language. These statements may also include defined functions that are not syntactically consistent with the procedural programming language. The defined functions may be associated with a given function that is defined according to the procedural programming language. The given function may relate to a geometric design of an object. The methods may identify inputs and outputs to this given function, and may build a dependency graph that relates this given function to other functions, based on the inputs and/or outputs of the given function. The methods may delay evaluating the given function until a triggering event occurs, at which time the methods may evaluate the given function to produce the output.

BACKGROUND

Computer-aided design and engineering packages are increasingly usedwithin the industry to expedite designing, prototyping, testing, andimproving various vehicles and systems. Generally, relatively powerfulcomputing systems may run these design and engineering packages.However, as designs for these vehicle and systems become more complex,these computing systems may become increasingly burdened, and thereforemay become less responsive to user commands.

SUMMARY

It should be appreciated that this Summary is provided to introduce aselection of concepts in a simplified form that are further describedbelow in the Detailed Description. This Summary is not intended to limitthe scope of the claimed subject matter.

This description provides tools for lazy evaluation of geometricdefinitions of objects within procedural programming environments.Computer-based methods provided by these tools may parse input programcode that includes statements that are syntactically consistent with aprocedural programming language. These statements may also includedefined functions that are not syntactically consistent with theprocedural programming language. The defined functions may be associatedwith a given function that is defined according to the proceduralprogramming language. The given function may relate to a geometricdesign of an object. The methods may identify inputs and outputs to thisgiven function, and may build a dependency graph that relates this givenfunction to other functions, based on the inputs and/or outputs of thegiven function. The methods may delay evaluating the given functionuntil a triggering event occurs, at which time the methods may evaluatethe given function to produce the output.

The features, functions, and advantages discussed herein may be achievedindependently in various embodiments of the present description or maybe combined in yet other embodiments, further details of which can beseen with reference to the following description and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates systems or operating environments for the lazyevaluation of geometric definitions of objects within proceduralprogramming environments.

FIG. 2 illustrates example applications for the lazy evaluation ofgeometric definitions of objects within procedural programmingenvironments.

FIG. 3 illustrates additional aspects of program code/script for thelazy evaluation techniques described herein, along with relatedprocessing that a design application may perform according to thesetechniques.

FIG. 4 illustrates components and process flows for performing lazyevaluations as described herein.

DETAILED DESCRIPTION

The following detailed description provides various tools and techniquesfor lazy evaluation of geometric definitions of objects withinprocedural programming environments. This description proceeds withreference to various drawings, and to numerals appearing within thedrawings. The first digit within a given reference numeral indicates thedrawing in which that numeral first appears.

FIG. 1 illustrates systems or operating environments, denoted generallyat 100, for the lazy evaluation of geometric definitions of objectswithin procedural programming environments. For ease of description, andwithout limiting possible implementations, the term “lazy” as usedherein refers to deferring the evaluation of expressions or functionsuntil some event or trigger occurs.

This description generally refers to evaluating functions. However, thisterminology is chosen only for example, and not to exclude equivalentexpressions or to limit possible implementations. For example, theterminology “construction of a class instance” may be suitable as well.

These systems 100 may include one or more vehicle design systems 102.Vehicle design systems may be configured to support interactions 104with one or more users 106. For example, and without limitation, theusers 106 may be engineers, system designers, programmers, analysts, orthe like. In addition, subsequent drawings provide more detail andexamples relating to the interactions 104.

FIG. 1 illustrates several examples of platforms that may host thevehicle design systems 102. These examples may include one or moreserver-based systems 108, one or more portable computing systems 110(whether characterized as laptops, notebooks, or other types of mobilecomputing systems), and/or one or more relatively stationary desktopcomputing systems 112.

Implementations of this description may include other types of platformsas well, with FIG. 1 providing non-limiting examples. For example, thedescription herein contemplates other platforms for implementing thevehicle design systems, including but not limited to wireless personaldigital assistants, smartphones, or the like. Thus, FIG. 1 provides thegraphical elements used to depict these various components only tofacilitate illustration, and not to limit possible implementations ofthe description herein.

As detailed elsewhere herein, the vehicle design systems 102 may enablethe users to interactively design, model, and/or prototype variouscomplex mechanical systems, such as aircraft, boats, vehicles,spacecraft or the like. Generally, the vehicle design systems maysupport design efforts relating to any air-based, ground-based, orsea-based vehicles.

Turning to the vehicle design systems 102 in more detail, these systemsmay include one or more processors 114, which may have a particular typeor architecture, chosen as appropriate for particular implementations.The processors 114 may couple to one or more bus systems 116 that arechosen for compatibility with the processors 114.

The vehicle design systems 102 may include one or more instances ofcomputer-readable storage media 118, which couple to the bus systems116. The bus systems may enable the processors 114 to read code and/ordata to/from the computer-readable storage media 118. The media 118 mayrepresent storage elements implemented using any suitable technology,including but not limited to semiconductors, magnetic materials, optics,or the like. The media 118 may include memory components, whetherclassified as RAM, ROM, flash, or other types, and may also representhard disk drives.

The storage media 118 may include one or more modules 120 ofinstructions that, when loaded into the processor 114 and executed,cause the vehicle design systems 102 to enable the users 106 toparticipate in design actions. For example, the modules 120 may includeone or more design applications that provide an interactive experiencefor the users 106. These modules 120 may implement the variousalgorithms and models described and illustrated herein.

Turning to the example design application 120 in more detail, the designapplication may enable the users 106 to provide or generate instances ofprogram code or script, denoted generally at 122. Generally, the programcode/script 122 represents sequences of instructions that the designapplication 120 may execute while supporting the efforts of the users106. Various examples of the program code/script 122 are describedbelow.

As shown in FIG. 1, the design application 120 may include componentsrelated to lazy evaluation processing, denoted generally at 124. Thelazy evaluation components 124 may cooperate with components 126, whichgenerally represent subsystems and utilities related to supporting agiven imperative programming language. Examples of such utilities mayinclude compilers, developers toolkits, or the like. Illustrative, butnon-limiting examples of programming languages may include Python,Jython, Java, C, Groovy, or the like. Generally, these programminglanguages are procedural in nature, and may be chosen as appropriate forparticular design applications.

FIG. 1 also illustrates at 128 various support libraries associated withthe imperative language processing components 126. These supportlibraries 128 may include libraries of built in functions, for example.

The lazy evaluation processing components 144 may also cooperate withcomponents 130 that support programming operations typically associatedwith functional or declarative languages. Typically, users 106 (e.g.,engineers, scientific analysts, or other highly-trained designpersonnel) are trained and comfortable with procedural or imperativeprogramming languages. However, as described in further detail herein,designs of complex mechanical systems or vehicles may involve theconstruction and recomputing of computationally-intensive geometricmodels. Recomputing the entire geometric model for each change or updatemade by the user 106 may consume considerable system resources (e.g.,processor 114 cycles). In some cases, delays entailed by these recomputefunctions may decrease system responsiveness and degrade the overalluser experience. For example, a previously interactive user experiencemay become less interactive, with corresponding increases in user waittimes.

As shown in FIG. 1, the lazy evaluation processing components 124 maycooperate with the imperative language processing components 126 and thefunctional language processing components 130 to generate programoutputs 132 in response to the input program code/script 122. Morespecifically, the interactions 104 may represent any number of discreteinstances in which the user 106 may provide program code/script 122 orother commands to the system 102, and received in response thereto theprogram outputs 132. Subsequent drawings and discussion provide moredetail on the processing performed by these components.

Having described the overall systems or operating environments 100, thediscussion now proceeds to a description of illustrative examples thatapply the tools and techniques for lazy evaluation of geometricdefinitions of objects within procedural programming environments. Thisdiscussion is now presented with FIG. 2.

FIG. 2 illustrates example applications, denoted generally at 200, forlazy evaluation of geometric definitions of objects within proceduralprogramming environments. To facilitate reference and description, butnot to limit possible implementations, FIG. 2 may carry forward someitems described previously, as denoted by similar reference numbers.

FIG. 2 depicts an example user (e.g., 106) interacting with a suitabledesign application (e.g., 120) in connection with designing an exampleobject or device, as represented generally by the dashed line 202. FIG.2 provides an example in which this device is a table 204. However,possible implementations may apply this description to design any numberand/or type of different devices, vehicles, or systems, and FIG. 2provides the example shown only for ease of description.

As described previously in FIG. 1, interaction 104 may represent anynumber of instances in which the user may provide program code/script(e.g., 122) to the design application 120, and may receive programoutputs (e.g., 132) in response thereto. For example, the programcode/script instances 122 may represent commands given by the user toadd new elements to an ongoing design, to modify some aspect of existingdesign elements, to delete design elements, or (more generally) toprovide any number or type of arbitrary commands or directives to thedesign application 120. The program outputs 132 may take any suitableform, including but not limited to, visual presentations of geometricmodels of an ongoing design, recomputed parameters or visualizationsassociated with these parameters, or the like.

Turning to the example device being designed (e.g., the table 204), thistable 204 may be modeled geometrically as having a tabletop portion 206and a plurality of leg elements 208. The design application 120 maycharacterize and model various subcomponents of the table within aconvenient Cartesian coordinate system. Turning to the tabletop 206 asan example, the design application may track parameters indicating alength 210 of the tabletop, a thickness 212, and/or a width 214.Although not shown explicitly in FIG. 2, the design application maytrack similar parameters as related to the various leg elements 208.

In general, the design application 120 may maintain a geometricdefinition 216 corresponding to a device or system (e.g. the table 204)being designed with the design application 120. In addition, thegeometric definition may include respective definitions for varioussubcomponents included within the overall device or system. In theexample shown, the geometric definition 216 for the table may include atleast a sub-definition element 218 for the tabletop and one or moresub-definition elements 220 for the table legs. In turn, the tabletopdefinition element 218 may include a sub-element 222 that specifies theappropriate x, y, and z values that define the geometric model for thetabletop. Likewise, the leg definition element 220 may define asub-element 224 that specifies the appropriate x, y, and z values thatdefine the geometric models for the various table legs.

As described in further detail in the examples below, the user 106 maygive various commands, for example in the form of the programcode/script elements 122, that may change, add, or delete variousaspects of the geometric definition 216, or sub-elements thereof. Inturn, the design application 120 may generate new program outputs 132 inresponse to these commands. More specifically, the design application120 may cooperate with the lazy evaluation module 124 to improve theefficiency with which the design application may generate the programoutputs.

As examples of the foregoing improvements in efficiency, assume that theuser 106 issues commands in the form of program code that changes thelength 210 of the tabletop 206. In response to these commands, thedesign application may identify which geometric aspects of the table areimpacted by the change in the length of the tabletop. In this example,the design application may determine that only the geometric definitionof the tabletop element (e.g., 218) is impacted by the change in length,and may further determine that the geometric definitions of the varioustable leg elements (e.g., 220) remain unchanged. In turn, the designapplication may refer to the geometric definition 218 for the tabletop,and may recompute only the impacted geometric elements 222. However, thetable leg element 220 and related geometric definitions 224 may remainunchanged. In general, the design application 120 may decrease user waittime by avoiding the recompute operations associated with unchangedelements.

In an example in which the user lengthens the tabletop sufficiently, thedesign application 120 may add additional table legs 208, as may bespecified by applicable design rules. In such cases, the designapplication 120 may instantiate additional definition elements 220and/or 224 for the added table legs, but need not recompute thegeometric definitions of any of the table legs.

In another example, assume that the user 106 issues commands that changethe thickness 212 of the tabletop 206. In this example, the designapplication 120 may again determine that this change in tabletopthickness impacts only the geometric definitions of the tabletop, butmay also determine that the geometric definitions of the table legs 208remain unchanged. Accordingly, the design application may improve theefficiency of the recompute operation that results from this change byrecomputing only the geometric definitions of the tabletop elements.

Having described the operational examples provided in FIG. 2, thediscussion now proceeds to a description of additional aspects of theprogram code/script and related processing by components of the designapplication. This description is now provided with FIG. 3.

FIG. 3 illustrates additional aspects, denoted generally at 300, of theprogram code/script and related processing by components of the designapplication. To facilitate reference and description, but not to limitpossible implementations, FIG. 3 may carry forward some items describedpreviously, as denoted by similar reference numbers. For example, FIG. 3carries forward the program code/script 122, as well as the lazyevaluation processing component 124, the imperative language processingcomponent 126, and the functional language processing component 130.

Turning to the program code/script 122 in more detail, the program codemay include one or more statements as supported by a given programminglanguage, denoted as native code 302 in FIG. 3. Put differently, thenative code 302 may be consistent with syntax rules defined by the givenprogramming language. The program code may also include one or moreadditional defined functions, denoted at 304. These additional definedfunctions may be added to the stream of program code 122 in order tofacilitate the tools and techniques described herein. This descriptionnow proceeds with several source code examples to illustrate these toolsand techniques.

The following set of examples uses syntax defined by the Python/Jython(referred to as “Python”) programming languages. As a starting point,consider the existing behavior of this example of unmodified Pythonlanguage. This set of expressions would produce the following behavior:

-   a=1-   b=2-   print “c is now”, c    Executing these statements would produce as output:-   >>>c is now 3

The next several statements change one of the values used by theexpression to define “c”:

-   a=5-   print “c is now”, c    Executing these statements would produce as output:-   >>>c is now 3

In the preceding example, the statement c=a+b was not re-evaluated, eventhough one of its input parameters changed values. This behavior may betypical for Python or any procedural programming language.

Now, consider a new example including a defined function called “Rule”added to the Python code:

-   a=1-   b=2-   c=Rule(lambda: a+b)-   print “c is now”, c    Executing these statements would produce as output:-   >>>c is now 3

Continuing this example, the next sequence of statements may change oneof the inputs to the rule for c, as follows:

-   a=5-   print “c is now”, c    Executing these statements would produce as output:-   >>>c is now 7

Having provided the foregoing examples, several observations are noted.First, the “lambda” keyword included in the above example statementsrefers to a predefined Python function that converts an input expressioninto an unnamed function. Second, the function or class “Rule” is addedto the default Python code, thereby augmenting the default Python codeto perform the assessing described herein. Thus, the function “Rule”provides an example of the defined functions 304 shown in FIG. 3.However, it is noted that the name “Rule” is provided as an exampleonly, and implementations of the description herein may use any suitablename. Typically, implementations of this description may choose namesfor the functions 304 that do not otherwise appear in syntax rules forthe procedural language in which the native code 302 is written.Generally, the key word mechanism (e.g., “Rule”) may refer to orincorporate any programming statement that may be expressed as afunction (e.g., the lambda function in the previous example).

As shown in FIG. 3, the program code/script 122 may be input to the lazyevaluation processing component 124. In turn, the component 124 mayidentify any defined functions appearing in the input programcode/script (e.g., “Rule”), and route them to the functional languagecomponent 130, as indicated at 304 a. In turn, the functional languagecomponents 130 may process the defined functions and any inputarguments, as represented generally at 306.

The lazy evaluation processing may also route native code to theimperative language component 126 as denoted at 302 a. In turn, theimperative language components 126 may process the native code and anyinput arguments, as represented generally at 308. Finally, the programoutputs 132 may include the results of the functional statementprocessing represented at 306 and the imperative statement processingrepresented at 308.

The foregoing examples illustrate how the tools and techniques describedherein may extend an underlying dynamic programming language (e.g.,Python) to support an additional or de fined function (e.g., “Rule”).This function may be a built-in function or class with full access to acontaining namespace or module level namespace, depending on the levelin which the rule is embedded within a given sequence of source codestatements. A given rule object may depend on other classes, objects, orfunctions in the same namespace, and this namespace (whether the modulenamespace or a class-instance namespace) may be enhanced to trackdependencies.

A given rule maintains state information about itself. For example, thisstate information may enable the rule to track or determine whether ithas been evaluated, whether any errors occurred in this evaluation,whether results of such evaluations have been cached, whether the ruledepends on a variable whose changes in value may not be readily apparentto the rule, or the like. Rules as described herein may allow for lazyevaluation or strict evaluation of a function and/or constructor. Inexample implementations, users may select whether to perform lazyevaluation or strict evaluation by interacting with a toggle or flagmechanism specifies lazy or strict evaluation. A single given rule mayexist without depending on any other rules. However, in cases in which agiven rule depends upon one or more other rules, the rules may notexplicitly depend upon one another, but may instead depend uponkeywords. These keywords may reference other rules, thereby creatingimplicit dependencies between rules. A set of given rules may bedeclarative in nature, and that they have no predetermined order ofexecution. A set of rules with these implicit dependencies can be storedin a single namespace that is enhanced to mediate between the rules, andto track dependencies between the rules.

Rules may depend on keys read from the namespace. These keys may beother rules, but they may also be variables or functions. For example,the statement c=Rule(lambda: a+b) defines a rule that is associated withthe keyword “c”. When this rule is executed for the first time, “a” and“b” will be retrieved from the namespace, and as a result, the rule willupdate its state information to indicate that it depends on “a” and “b”,without regard to the values “a” and “b”.

Now, assuming a second rule: d=Rule(lambda: c+3), this rule will beassociated with the keyword “d”. When this rule is executed, it willretrieve “c”, without knowing (or caring) that “c” is also a rule.However, by asking for “c”, the first rule associated with “c” willexecute as appropriate or return a cached value. The dependencies of anyfunctions upstream and/or downstream a given rule (discussed in moredetail below) are defined implicitly when the rule is created.

As illustrated in the above examples, the action of retrieving “c” fromthe namespace may cause or trigger evaluation of “c”. By using thismechanism to evaluate expressions, the user may obtain additionalinsight into when functions wrapped by these “Rule” statements areexecuted. In addition, the mechanisms described herein may definerespective private namespaces for different rules and their parameters,to prevent interference or conflicts with other user defined namespaces.Generally, the lazy evaluation mechanism may operate independently ofthe types specified for any particular parameter.

In the foregoing examples, the syntax of the native code is unchanged.In this manner, the lazy evaluation components 124 may support lazyevaluation concepts within an overall imperative programming framework,without requiring the user to write code in an unfamiliar functionallanguage or to use an awkward application program interface (API), orprogramming syntax.

Additionally, in the examples above, the line of code that wasencapsulated within the “Rule( )” was a function to be evaluated. Inthese examples, the “Rule( )” encapsulates a function because the Rulethat is created describes some sort of dependency between differentvariables. In these examples, the expression for “c” depends on theinput arguments “a” and “b”. The function “lambda” in these examples isa built-in function in the Python language that changes certainexpressions into an unnamed function, and therefore defers or delaysevaluation of the expression.

This description also provides additional examples of source codeincorporating the added function or class “Rule”. The lazy evaluationcomponent 124 may process these and other examples of the programcode/script 122:

-   def add(x, y):    -   print “Hi”    -   return x+y-   a=1-   b=2-   d=Rule( lambda: add(a, b))-   print “d is now”, d    Executing these statements would produce this output:-   Hi-   >>>d is now 3    Asking for the same value d again would return the cached value:-   >>>d is now 3    In this example, the function “add” was not re-executed, and hence    the execution output “Hi”.

In the next example, changing one of the input variables results inre-evaluation of the rule, when the value of d is requested:

-   a=12-   print “d is now”, d    Executing these statements would produce the output:-   Hi-   >>>d is now 14

The lazy evaluation component 124 may also track dependencies of therule definition, in this example, the function “add”. This means thatthe source code may redefine the function “add” later, and this wouldcause a re-evaluation of the expression “d” the next time that the valueof “d” was requested. Continuing the previous example, redefining thefunction “add” may result in the following:

-   def add(x, y):    -   print “Oy”    -   return (x−y)-   print “d is now”, d    Executing these statements may produce the output:-   Oy-   >>>d is now 10

Even though these examples used integers to demonstrate examplefunctionality, the description herein may be used with any system- oruser-defined data type, including objects. Another example typicalscenario that may leverage this lazy mechanism to reduce computations intime intensive geometric operations follows:

length = 250 span = 120 body = Rule( Fuselage( length ) )   # result isa solid model wing = Rule( Wing( span ) )  # result is a solid modelb797 = Union( body, wing )  # Boolean union of the two solids

In this example, these statements are fighting different rules fordefining geometric definitions for an aircraft “body” and for anaircraft “wing”. Changing the span of the wing element would not causere-computation of the body element, thereby saving the time andresources that would otherwise be devoted to recomputing the geometricdefinition of the body element. Thus, this example elaborates further onthe table example, as shown previously in FIG. 2.

The rule mechanism can also be embedded into object definitions, asshown by the following example:

 class MyObject(Rules):   def _init_(self):    Rules._init_(self)   self.a = 1    self.b = 2    self.c = self.Rule(self.add)   defadd(self):    print “Hi”    return self.a + self.b g = MyObject( ) #Creates and instance of the class MyObject which inherits from Rulesprint g.c # c is a rule based on the function “add”Executing the above statements may result in the following output:

-   Hi-   >>>3    A second evaluation of the same property returns a cached value:-   print g.c    Thus, executing the above statement produces the following output:-   >>>3    In the foregoing example, note that the output did not include the    string “Hi”, which indicates that the function “add” was not called.

Continuing this example, the following code changes one of the inputs asfollows:

-   g.a=2-   print g.c    Executing these statements produces the following output:-   “Hi”-   >>>4    The preceding example printed the string “hi”. This result occurred    because the lazy evaluation component 124 detected that the value of    “c” was out of date, because the value of “a” had changed.    Accordingly, the evaluation component 124 called the function “add”    to update the value of “c”.

The foregoing examples are provided only for use of description inillustrating example dependencies between variables. However,implementations of the description herein may define dependencyrelationships having arbitrary complexity.

Having described the additional aspects of the program code/script andrelated processing by components of the design application in connectionwith FIG. 3, the discussion now proceeds to a description ofillustrative components and process flows for performing lazyevaluation. This discussion is now presented with FIG. 4.

FIG. 4 illustrates components and process flows, denoted generally at400, for performing lazy evaluations as described herein. To facilitatereference and description, but not to limit possible implementations,FIG. 4 may carry forward some items described previously, as denoted bysimilar reference numbers. For example, FIG. 4 carries forward theexample user 106, the program code/script 122, as well as the lazyevaluation component 124, and the program outputs 132. In the exampleshown, the lazy evaluation component 124 may implement at least portionsof the various components and process/data flows in FIG. 4.

Turning to FIG. 4 in more detail, an evaluator mechanism 402 may receiveinput program code/script (e.g., 122), which may include any number ofrespective statements. The evaluator 402 may digest or parse thecontents of these statements into perspective contents or tokens, whichare denoted generally at 404. The evaluator may or may not execute thesestatements, in different possible scenarios. As described previously,the input program code/script may include native code statements (e.g.,302 in FIG. 3), and may also include additional defined functions (e.g.,304 in FIG. 3). In instances where statements within the input programcode/script contain additional defined functions (e.g., a “Rule” in thepreceding examples), the evaluator mechanism may process contents ofthese statements without evaluating the statements as executableexpressions. In turn, the evaluator 402 may pass these contents 404 toan inference component 406.

The inference component 406 processes the contents received from theparser 402, and infers the inputs and outputs of any expression orfunction defined within the contents. For example, in cases whereadditional functions define rules, the inference component 406 may inferthe inputs and/or outputs of expressions or functions defined by suchrules. FIG. 4 denotes examples of such functions at 408, denotes inputsto such functions puts at 410, and denotes outputs from such functionsat 412. In turn, the inference component 406 passes the function, alongwith its inputs and outputs, to a dependency tracking mechanism 414.

The dependency tracking mechanism 414 analyzes inputs and outputs ofgiven functions, and builds a dependency graph 416 indicating how agiven function relates to zero or more other functions. For example, thedependency graph 416 may be “null”, in the sense that the graphrepresents a rule or function whose inputs are not outputs from anotherrule or function. In example implementations, the graph 416 may be adirected acyclic graph.

In some scenarios, a given function may depend one zero or more upstreamfunctions 418, in the sense that outputs 420 from the upstream functionsare inputs to the given function. For example, a given function may bethe starting point of a dependency graph, and in these cases, nofunctions would be upstream of the given function. In other cases, thegiven function may depend on one or more upstream functions.

In addition, one or more downstream functions 422 may depend on thegiven function, in the sense that outputs from the given function areinputs 424 to the downstream functions. In general, the dependencytracking mechanism 414 may track dependencies between inputs and outputsof a plurality of different functions, as well as definitions of thedifferent functions themselves.

By analyzing the dependency graph 416, the dependency tracking mechanism414 may infer when an input parameter to a given function has changed,thereby possibly driving a reevaluation of the given function. When theinput parameter changes, the dependency tracking mechanism may mark asout of date the results of any functions that are downstream from thisinput parameter. For example, the dependency tracking mechanism maymodify the dependency graph to indicate which inputs and/or outputs areout of date. In addition, the dependency tracking mechanism may processthe dependency graph to identify any circular references existingbetween the inputs and outputs of different functions. If the dependencytracking mechanism locates any circular references, then the mechanismmay report an appropriate error message to a user. In turn, the user maycorrect or resolve the circular reference before the dependency trackingmechanism processes the graph further.

The dependency tracking mechanism 414 may track dependencies betweenrules or functions implicitly, with the dependencies being updated whilethe rules or functions are executing. Each Rule is responsible for onefunction. The rule decides when to execute the function (e.g., based onwhether a value has been cached for the function, whether the function'supstream dependencies have changed values, or the like). Just before theRule executes the function, the Rule will register that it is monitoringthe enhanced namespace where the function was defined. The enhancednamespace will tell any Rule that is currently registered every time agiven key is accessed. Immediately after the function is executed, theRule will remove itself as a listener. The Rule mechanism may executethis namespace registration code immediately before and after thefunction executes. The Rule class may be extended to add any othercustomized code that would execute before or after the function. Forexample, you could add code that would write out information to a logfile immediately before and/or after the function was executed.

In this manner, the dependency tracking mechanism may relieveprogrammers from explicitly defining relationships between rules.Instead, the programmers may write rules that use various inputs, notexplicitly defining relationships between rules and other rules, orbetween rules and various other inputs.

The dependency tracking mechanism may relieve programmers from checkingthat specified dependencies are consistent with the actual code inaddition, the tracking mechanism allows for scalability: if a programmerwishes to make a 600 line function into a rule, it would be difficult todefine all of the dependencies within this function.

If the dependencies are defined explicitly, then a rule would depend onall of those explicitly defined dependencies. However, if the tendenciesare created implicitly during execution of the rule, then the rule willdepend only on the variables used to evaluate the rule at runtime, as anexample, consider the following scenario:

-   def function( ):    -   if a>0:        -   return b    -   else        -   return c-   a=1-   b=2-   c=3-   d=Rule(lambda: function( ))-   print‘d=’, d-   >>d=2

If dependencies between the values a, b, c, and d were definedexplicitly, d would depend on a, b and c. However, in executing theabove scenario, if the value of c were to change, the function wouldstill return 2. The code involving c was never reached during execution,given the values assigned to a and b. By implicitly trackingdependencies of the variables (i.e., during execution), d only dependson the run-time values of a and b, which is more correct in executionscenarios.

A delay mechanism 426 may receive the dependency graph, and may delayevaluation of given functions within that dependency graph. Generally,the delay processing mechanism 426 may defer evaluating a given functionuntil receiving an external trigger to evaluate the function. FIG. 4denotes an example trigger at 428. Non-limiting examples of a trigger ortriggering event may include explicit requests for the output of thegiven function, changes in input values upon which the given functionmay depend, or the like.

Once the trigger event has occurred, a decision block 430 may determinewhether a valid output value for the given function already exists in acache. Put differently, decision block 430 may evaluate whether anup-to-date output (i.e., not rendered obsolete by changing input valuesupstream of the given function) resides in the cache. If so, a Yesbranch 432 leads to block 434, which represents retrieving the requestedoutput from the cache. FIG. 4 denotes an example cache at 436, andgenerally represents outputs obtained from the cache at 438. In turn,block 440 represents returning the requested outputs as program outputs132. In this manner, the process is shown in FIG. 4 may avoidre-evaluating a function when none of its inputs have changed, byretrieving previously-calculated results for the function using, forexample, memoization techniques.

Returning to decision block 430, if the cache does not contain acurrent, valid output, a No branch 442 leads to block 444. Block 444represents evaluating one or more rules to obtain results responsive tothe trigger 428. Processing may reach block 444 for several differentreasons, including for example, changing inputs to a given rulerendering obsolete the contents of the cache. In another scenario, thecache may not contain any relevant results, whether obsolete or not. Inany case, the mechanisms shown in FIG. 4 may reevaluate a given rulewhen one of its inputs has changed, when a function associated with therule changes, or when the function has not been evaluated previously.

Once block 444 has evaluated the functions and obtained results, block444 may store these results in the cache 436, as represented at 446. Inaddition, processing may proceed from block 444 to block 440, to returnthe newly-evaluated results as program outputs 132.

Returning briefly to the table example shown in FIG. 2, this example mayillustrate operations of different functions, as well as dependenciesbetween these functions. For example, assume that one function governsthe geometric definitions of the four table legs 208, and assume thatanother function governs the geometric definition of the tabletop 206.In this example, the dependency graph 416 may specify that the tabletopfunction depends upon the Cartesian coordinates input parameters for thetabletop itself, while the table leg function depends upon the Cartesiancoordinates of the table legs. Accordingly, the dependency graph 416 mayindicate that changes to the Cartesian coordinates of the table legswould have no effect upon the geometric definition of the tabletop. Inaddition, the dependency graph 416 may indicate that changes to theCartesian coordinates of the tabletop would have no effect upon thegeometric definition of the table legs. Therefore, if the user changesthe Cartesian coordinates of the table legs, the dependency graph wouldindicate that only the geometric definitions of the table legs are to beupdated.

The subject matter described above is provided by way of illustrationonly and does not limit possible implementations. Various modificationsand changes may be made to the subject matter described herein withoutfollowing the example embodiments and applications illustrated anddescribed, and without departing from the true spirit and scope of thepresent description, which is set forth in the following claims.

1. A computer-based method comprising at least: evaluating input programcode that includes at least one rule, wherein the rule wraps a functiondefined by a procedural programming language; delaying evaluation of thefunction, in response to the rule, until an occurrence of at least onetriggering event; and evaluating at least the function to produce atleast one output in response to the triggering event, wherein thefunction relates to a geometric design of at least one object.
 2. Thecomputer-based method of claim 1, further comprising identifying atleast one input and at least one output to the function, and building adependency graph that relates the function to at least a secondfunction, based on the input or the output to the function.
 3. Thecomputer-based method of claim 2, wherein building a dependency graphincludes relating the function to at least one upstream function thatgenerates at least one output that is the input to the function.
 4. Thecomputer-based method of claim 2, wherein building a dependency graphincludes relating the function to a least one downstream function thatreceives as input the output of the function.
 5. The computer-basedmethod of claim 1, wherein delaying evaluation of the function includesdeferring evaluation of the function until the output of the function isrequested.
 6. The computer-based method of claim 1, wherein delayingevaluation of the function includes deferring evaluation of the functionuntil at least the input to the function has changed.
 7. Thecomputer-based method of claim 1, further comprising marking as out ofdate at least one cached output of the function, in response todetecting that at least one input to the function or the function haschanged values.
 8. The computer-based method of claim 2, furthercomprising analyzing the dependency graph, and further comprisingmarking as out of date at least one cached output of the secondfunction, in response to detecting that at least one input to the secondfunction has changed values.
 9. The computer-based method of claim 1,further comprising receiving a request for an output of the function,and further comprising determining whether a valid instance of therequested output exists in a cache.
 10. The computer-based method ofclaim 9, further comprising retrieving the requested output from thecache.
 11. The computer-based method of claim 9, further comprisingdetermining that the cache contains an out of date instance of therequested output, reevaluating the function, and re-caching a refreshedinstance of the requested output.
 12. A vehicle design system comprisingat least: at least one processor; at least one computer readable storagemedium coupled to communicate with the processor, the computer readablestorage medium including at least one design application, wherein thedesign application includes: at least one lazy evaluation componentadapted to: evaluate input program code that includes at least onestatement that is syntactically consistent with a procedural programminglanguage, and that includes at least one defined function that isassociated with a function defined by the procedural programminglanguage; identify at least one input and at least one output to thefunction; build a dependency graph that relates the function to at leasta second function, based on the input or the output to the function;delay evaluation of the function, in response to the defined function,until an occurrence of at least one triggering event; and evaluate atleast the first function to produce the output in response to thetriggering event, wherein at least the function relates to a geometricdesign of least one object; at least one imperative language componentadapted to receive and process the least one statement; and at least onefunctional language component adapted to receive and process the definedfunction and the function.
 13. The vehicle design system of claim 12,wherein the lazy evaluation component is for defining a geometricdefinition of at least part of the object using the first instance ofthe defined function, and is for defining a geometric definition of atleast a further part of the object using a second instance of thedefined function used in connection with the second function.
 14. Thevehicle design system of claim 13, wherein the lazy evaluation componentis for detecting a change in the input to the function, for determiningthat the change to the input affects the function and not the secondfunction, and for reevaluating the first function and not the secondfunction.
 15. At least one computer readable storage medium containingcomputer-executable instructions that, when loaded into at least oneprocessor and executed, cause the processor to perform a methodcomprising: evaluating input program code that includes at least onestatement that is syntactically consistent with a procedural programminglanguage, and that includes at least one rule that is not syntacticallyconsistent with the procedural programming language, wherein the rule isassociated with a first function defined by the procedural programminglanguage; identifying at least one input and at least one output to thefirst function; building a dependency graph that relates the firstfunction to at least a second function, based on the input or the outputto the first function; delaying evaluation of the first function, inresponse to the rule, until an occurrence of at least one triggeringevent; and evaluating at least the first function to produce the outputin response to the triggering event, wherein at least the first functionrelates to a geometric design of a least one object.
 16. The computerreadable storage medium of claim 15, further comprising instructions forreceiving a trigger event with respect to the first function, andfurther comprising instructions for determining whether a valid instanceof the output of the first function exists in a cache.
 17. Thecomputer-based method of claim 16, further comprising instructions forretrieving the output from the cache.
 18. The computer-based method ofclaim 16, further comprising instructions for determining that the cachecontains an out of date instance of the requested output, reevaluatingthe first function, and re-caching a refreshed instance of the requestedoutput.
 19. The computer-based method of claim 15, wherein theinstructions for building a dependency graph include instructions forrelating the first function to a least one upstream function thatgenerates at least one output that is the input to the first function.20. The computer-based method of claim 15, wherein the instructions forbuilding a dependency graph include instructions for relating the firstfunction to a least one downstream function that receives as input theoutput of the first function.